A fallacy is a component of an argument that is demonstrably flawed in its logic or form, thus rendering the argument invalid (except in the case of begging the question) in whole.
In logical arguments, fallacies are either formal or informal. Because the validity of a deductive argument depends on its form, a formal fallacy (or logical fallacy) is a deductive argument that has an invalid form, whereas an informal fallacy is any other invalid mode of reasoning whose flaw is not in the form of the argument.

Beginning with Aristotle, informal fallacies have generally been placed in one of several categories, depending on the source of the fallacy. There are fallacies of relevance, fallacies involving causal reasoning, and fallacies resulting from ambiguities.
A similar approach to understanding and classifying fallacies is provided by argumentation theory.
In this approach, an argument is regarded as part of an interactive protocol between individuals who are attempting to resolve a disagreement. The protocol is regulated by certain rules of interaction and violations of these rules are fallacies.

Recognizing fallacies in actual arguments may be difficult since arguments are often structured using rhetorical patterns that obscure the logical connections between assertions. As we illustrate with various examples, fallacies may also exploit the emotions or intellectual or psychological weaknesses of the interlocutor. Having the capability of recognizing logical fallacies in arguments will hopefully reduce the likelihood of such an occurrence.

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The classification of material fallacies widely adopted by modern logicians and based on that of Aristotle, Organon (Sophistici elenchi), is as follows:

Fallacy of Accident (also called destroying the exception or a dicto simpliciter ad dictum secundum quid) meaning to argue erroneously from a general rule to a particular case, without proper regard to particular conditions that vitiate the application of the general rule; e.g. if manhood suffrage be the law, arguing that a criminal or a lunatic must, therefore, have a vote.

Converse Fallacy of Accident (also called reverse accident, destroying the exception, or a dicto secundum quid ad dictum simpliciter) meaning to argue from a special case to a general rule.

Irrelevant Conclusion (also called Ignoratio Elenchi), wherein, instead of proving the fact in dispute, the arguer seeks to gain his point by diverting attention to some extraneous fact (as in the legal story of "No case. Abuse the plaintiff's attorney"). The fallacies are common in platform oratory, in which the speaker obscures the real issue by appealing to his audience on the grounds of

This fallacy has been illustrated by ethical or theological arguments wherein the fear of punishment is subtly substituted for abstract right as the sanction of moral obligation.

Begging the question (also called Petitio Principii or Circulus in Probando--arguing in a circle) consists in demonstrating a conclusion by means of premises that pre-suppose that conclusion. Jeremy Bentham points out that this fallacy may lurk in a single word, especially in an epithet, e.g. if a measure were condemned simply on the ground that it is alleged to be "un-English".

Fallacy of the Consequent, really a species of Irrelevant Conclusion, wherein a conclusion is drawn from premises that do not really support it.

Fallacy of False Cause, or Non Sequitur (L., it does not follow), wherein one thing is incorrectly assumed as the cause of another, as when the ancients attributed a public calamity to a meteorological phenomenon (a special case of this fallacy also goes by the Latin term post hoc ergo propter hoc; the fallacy of believing that temporal succession implies a causal relation).

Fallacy of Many Questions (Plurium Interrogationum), wherein several questions are improperly grouped in the form of one, and a direct categorical answer is demanded, e.g. if a prosecuting counsel asked the prisoner " What time was it when you met this man? " with the intention of eliciting the tacit admission that such a meeting had taken place. Another example is the classic line, "Is it true that you no longer beat your wife?"

Verbal fallacies are those in which a false conclusion is obtained by improper or ambiguous use of words. They are generally classified as follows.

Equivocation consists in employing the same word in two or more senses, e.g. in a syllogism, the middle term being used in one sense in the major and another in the minor premise, so that in fact there are four not three terms ("All fair things are honourable; This woman is fair; therefore this woman is honourable," the second "fair" being in reference to complexion).

Amphibology is the result of ambiguity of grammatical structure, e.g. of the position of the adverb "only" in careless writers ("He only said that," in which sentence, as experience shows, the adverb has been intended to qualify any one of the other three words).

Fallacy of Composition is a species of Amphibology that results from the confused use of collective terms. e.g. "The angles of a triangle are less than two right angles" might refer to the angles separately or added together.

Division, the converse of the preceding, which consists in employing the middle term distributively in the minor and collectively in the major premise.

Accent, which occurs only in speaking and consists of emphasizing the wrong word in a sentence. E.g., "He is a fairly good pianist," according to the emphasis on the words, may imply praise of a beginner's progress, or an expert's depreciation of a popular hero, or it may imply that the person in question is a deplorable violinist).

Figure of Speech, the confusion between the metaphorical and ordinary uses of a word or phrase.

Of other classifications of fallacies in general the most famous are those of Francis Bacon and J. S. Mill. Bacon (Novum Organum, Aph. 33, 38 sqq.) divided fallacies into four Idola (Idols, i.e. False Appearances), which summarize the various kinds of mistakes to which the human intellect is prone. With these should be compared the Offendicula of Roger Bacon, contained in the Opus maius, pt. i. J. S. Mill discussed the subject in book v. of his Logic, and Jeremy Bentham's Book of Fallacies (1824) contains valuable remarks. See Rd. Whateley's Logic, bk. v.; A. de Morgan, Formal Logic (1847) ; A. Sidgwick, Fallacies (1883) and other textbooks.

Fallacies are used frequently by pundits in the media and politics. When one politician says to another, "You don't have the moral authority to say X", this could be an example of the argumentum ad hominem or personal attack fallacy; that is, attempting to disprove X, not by addressing validity of X but by attacking the person who asserted X. Arguably, the politician is not even attempting to make an argument against X, but is instead offering a moral rebuke against the interlocutor. For instance, if X is the assertion:

The military uniform is a symbol of national strength and honor.

Then ostensibly, the politician is not trying to prove the contrary assertion. If this is the case, then there is no logically fallacious argument, but merely a personal opinion about moral worth. Thus identifying logical fallacies may be difficult and dependent upon context.

In the opposite direction is the fallacy of argument from authority. A classic example is the ipse dixit—"He himself said it" argument—used throughout the Middle Ages in reference to Aristotle. A modern instance is "celebrity spokespersons" in advertisements: a product is good and you should buy/use/support it because your favorite celebrity endorses it.

An appeal to authority is always a logical fallacy, though it can be an appropriate form of rational argument if, for example, it is an appeal to expert testimony. In this case, the expert witness must be recognized as such and all parties must agree that the testimony is appropriate to the circumstances. This form of argument is common in legal situations.

By definition, arguments with logical fallacies are invalid, but they can often be (re)written in such a way that they fit a valid argument form. The challenge to the interlocutor is, of course, to discover the false premise, i.e. the premise that makes the argument unsound.

The entries in the following list are neither exhaustive nor mutually exclusive; that is, several distinct entries may refer to the same pattern. As noted in the introduction, these fallacies describe erroneous or at least suspect patterns of argument in general, not necessarily argument based on formal logic. Many of the fallacies listed are traditionally recognized and discussed in works on critical thinking; others are more specialized.

Fallacious arguments involve not only formal logic but also causality.
Others involve psychological ploys
such as use of power relationships between proposer and interlocutor,
appeals to patriotism and morality, appeals to ego etc., to establish
necessary intermediate (explicit or implicit) premises for an argument.
Indeed, fallacies very often lay in unstated assumptions or implied
premises in arguments that are not always obvious at first glance.
One way to obscure a premise is through enthymeme.

We now give a few examples illustrating common errors in reasoning. Note that providing a critique of an argument has no relation to the truth of the conclusion. The conclusion could very well be true, while the argument itself is not valid. See argument from fallacy.

In the following, we view an argument as a dialogue between a proposer and an interlocutor.

This argument claims to prove that cheese is delicious. This particular argument has the form of a categorical syllogism. Any argument must have premises as well as a conclusion. In this case we need to ask what the premises are, that is the set of assumptions the proposer of the argument can expect the interlocutor to grant. The first assumption is almost true by definition: cheese is a foodstuff edible by humans. The second assumption is less clear as to its meaning. Since the assertion has no quantifiers of any kind, it could mean any one of the following:

All food is delicious.

Most food is delicious.

All food is delicious, except for spoiled or moldy food.

Some food is disgusting.

In any of the last three interpretations, the above syllogism would then fail to have validated its second premise. James may try to assume that his interlocutor believes that all food is delicious; if the interlocutor grants this then the argument is valid. In this case, the interlocutor is essentially conceding the point to James. However, the interlocutor is more likely to believe that some food is disgusting, such as a sheep's liver white chocolate torte; and in this case James is not much better off than he was before he formulated the argument, since he now has to prove the assertion that cheese is a unique type of universally delicious food, which is a disguised form of the original thesis. From the point of view of the interlocutor, James commits the logical fallacy of begging the question.

Here the problem is that the word good has different meanings, which is to say that it is an ambiguous word. In the premise, Barbara says that Andre is good at some particular activity, in this case tennis. In the conclusion, she says that Andre is a morally good person. These are clearly two different senses of the word "good". The premise might be true but the conclusion can still be false: Andre might be the best tennis player in the world but a rotten person morally. However, it is not legitimate to infer he is a bad person on the ground there has been a fallacious argument on the part of Barbara. Nothing concerning Andre's moral qualities is to be inferred from the premise. Appropriately, since it plays on an ambiguity, this sort of fallacy is called the fallacy of equivocation, that is, equating two incompatible terms or claims.

This argument has the appearance of an inference that applies transitivity of the two-placed relation is better than, which in this critique we grant is a valid property. The argument is an example of syntactic ambiguity. In fact, the first premise semantically does not predicate an attribute of the subject, as would for instance the assertion

In the strictest sense, a logical fallacy is the incorrect application of a valid logical principle or an application of a nonexistent principle:

Some drivers are men.

Some drivers are women.

Therefore, some drivers are both men and women.

This is fallacious. Indeed, there is no logical principle that states

For some x, P(x).

For some x, Q(x).

Therefore for some x, P(x) and Q(x).

An easy way to show the above inference is invalid is by using Venn diagrams. In logical parlance, the inference is invalid, since under at least one interpretation of the predicates it is not validity preserving.